Methods for modeling the Ornstein-Uhlenbeck process

Pashko, A. O., Ianevych, T. O. (2019). Methods for modeling the Ornstein-Uhlenbeck process. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics(3), 24–29. https://doi.org/10.17721/1812-5409.2019/3.3

Two methods of modeling for the Ornstein-Uhlenbeck process are studied in the work. This process has many applications in physics, financial mathematics, biology. Therefore, it is extremely important to have instruments for modeling this process to solve various theoretical and practical tasks. The peculiarity of this process is that it has many interesting properties: it is Gaussian process, is a stationary process, is a Markov process, it is a solution of the Langevin stochastic equation, etc. Each of these properties allows you to apply different methods to this process modeling. We have considered only two methods, although there are many more. One method uses the fact that this process is Gaussian. Another is based on the Fourier expansion. For both of these methods there were specific conditions are obtained when these models satisfy the given levels of accuracy and reliability.Key words: Ornstein–Uhlenbeck process, modeling with given accuracy and reliability, centered gaussian process, Fourier series.Pages of the article in the issue: 24 - 29Language of the article: Ukrainian